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# If N, C, and D are positive integers, what is the remainder

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If N, C, and D are positive integers, what is the remainder  [#permalink]

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06 Nov 2012, 18:35
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If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.

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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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06 Nov 2012, 18:54
1. insufficient b/c D and C can be any number. adding +1 can change remainder completely.
ex: D =2 , C = 3 R = 2 ... D = 2+1 , C = 3+1 R = 3
2: sufficient b/c (ND + NC)/CN => ND/CN + NC/CN => ND/CN =>D/C + 1 => R5

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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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11 Sep 2013, 04:20
Can someone please help with a detailed explanation? Was able to get the answer right but don't really know how I arrived at it.

Thanks
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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14 Oct 2014, 13:11
1
1) insufficient
2) ND+NC/CN gives a remainder of 5.

ND + NC / CN = (D+C)/C

So we know that (D+C)/C gives a remainder of 5.

The idea here is that if you add any multiple of C to C then you will definitely get a multiple of C. For eg. 4 is a multiple of 2. So (4+2)/2 will give R=0.
In this case though we have a number added to C leaving a remainder of 5. This means that D is not divisible by C and that D must leave a remainder of 5. Eg. (5+0)/10 leaves a remainder of 5 . (5+10)/10 will leave a remainder of 5 also. So the remainder will always be in D in the equation (D+C). This means that D/C will also give us a remainder of 5. Sufficient.
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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28 Oct 2014, 12:10
Well, I am confused here and need some help.

I chose D.

Reason is as follows:
For statement A:
take D+1=12 and C+1=7 so 12/7 => remainder 5
if we take 11/6 => remainder is still 5

In the explanation above for D=CK + (K + 4), for different values of K, we are actually changing the value of D while keeping the value of C same. If the algebra calculations are correct and logic is correct, there must be some example to support this explanation.

We all agree to sufficiency of statement B.

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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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04 Nov 2014, 02:55
VeritasPrepKarishma wrote:
kingb wrote:
If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.

Stmnt 1: If D+1 is divided by C+1, the remainder is 5.

D+1 = (C+1)k + 5
D = Ck + (k + 4)
When D is divided by C, the remainder will vary with k.
If k = 0, remainder will be 4 (C is greater than 4)
If k = 1, remainder will be 5 (C is greater than 5)
If k = 2, remainder will be 6 (C is greater than 6)
etc

2) If ND+NC is divided by CN, the remainder is 5.
ND + NC = CN*k + 5
DN = CN*(k-1) + 5
D = C*(k-1) + 5/N
Now, N is a positive integer and remainder must be a positive integer too. The only value that N can take such that 5/N is a positive integer is 1. So N must be 1.
D = C*(k -1) + 5
When D is divided by C, remainder is 5.

Sorry to bother , I just want to ask ... N can't be 5 ? 5/N will still be integer i.e. 1
Could you please explain why only value N can take is 1?
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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04 Nov 2014, 21:03
VeritasPrepKarishma wrote:
kingb wrote:
If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.

Stmnt 1: If D+1 is divided by C+1, the remainder is 5.

D+1 = (C+1)k + 5
D = Ck + (k + 4)
When D is divided by C, the remainder will vary with k.
If k = 0, remainder will be 4 (C is greater than 4)
If k = 1, remainder will be 5 (C is greater than 5)
If k = 2, remainder will be 6 (C is greater than 6)
etc

2) If ND+NC is divided by CN, the remainder is 5.
ND + NC = CN*k + 5
DN = CN*(k-1) + 5
D = C*(k-1) + 5/N
Now, N is a positive integer and remainder must be a positive integer too. The only value that N can take such that 5/N is a positive integer is 1. So N must be 1.
D = C*(k -1) + 5
When D is divided by C, remainder is 5.

Sorry to bother , I just want to ask ... N can't be 5 ? 5/N will still be integer i.e. 1
Could you please explain why only value N can take is 1?

Actually it can take value 5 too. I will rewrite the solution given above soon.
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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04 Nov 2014, 21:15
nnitingarg wrote:
Well, I am confused here and need some help.

I chose D.

Reason is as follows:
For statement A:
take D+1=12 and C+1=7 so 12/7 => remainder 5
if we take 11/6 => remainder is still 5

In the explanation above for D=CK + (K + 4), for different values of K, we are actually changing the value of D while keeping the value of C same. If the algebra calculations are correct and logic is correct, there must be some example to support this explanation.

We all agree to sufficiency of statement B.

In statement 1, say if C+1 = 8 and D+1 = 21, remainder is 5.
C = 7 and D = 20, remainder is 6.
Not sufficient alone.
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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13 Aug 2015, 09:53
1
1) is clearly insufficient

2) (ND+NC)/CN = Q + 5

==> (D/C)+1 = Q + 5
(D/C) = Q + 4

Hence Sufficient . Is the above approach correct ? Don't quite understand the Solutions given above.
Many Thanks
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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13 Aug 2015, 21:09
bhatiavai wrote:
1) is clearly insufficient

2) (ND+NC)/CN = Q + 5

==> (D/C)+1 = Q + 5
(D/C) = Q + 4

Hence Sufficient . Is the above approach correct ? Don't quite understand the Solutions given above.
Many Thanks

No, it is not.

Take some simple numbers: 11 divided by 5 gives quotient as 2 and remainder as 1.

$$\frac{11}{5} \neq 2 + 1$$

So $$\frac{(ND+NC)}{CN} \neq Q + 5$$

Actually, ND + NC = Q*CN + 5
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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28 Aug 2015, 02:03
1- Statement 1 insuf, C and D could be lot of number possibilities
2- N(D+C)/CN = D+C/C = D/C +1 = Q + 5/C => D = QC +4 is this good ?
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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28 Aug 2015, 20:54
jimwild wrote:
1- Statement 1 insuf, C and D could be lot of number possibilities
2- N(D+C)/CN = D+C/C = D/C +1 = Q + 5/C => D = QC +4 is this good ?

I don't understand how you got Q + 5/C from Q*CN + 5.
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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19 Sep 2016, 09:39
OA is definitely wrong. Should be E.
you cannot write remainder(ND/NC) = remainder(D/C)

eg remainder(20/15) = 5, remainder(4/3) = 1
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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19 Sep 2016, 15:35
1
1
lifetantrik wrote:
OA is definitely wrong. Should be E.
you cannot write remainder(ND/NC) = remainder(D/C)

eg remainder(20/15) = 5, remainder(4/3) = 1

I agree. Let me expand this out to show the actual cases that prove insufficiency.

(1)
case 1: D = 19, C = 14. Obeys the statement, because when 20 is divided by 15, the remainder is 5. The answer to the question is also 5.
case 2: D = 28, C = 5. Obeys, the statement, because when 29 is divided by 6, the remainder is 5. The answer to the question, though, is 3. That's because when you divide 28 by 5, the remainder is 3.

(2)
case 1: D = 4, C = 3, N = 5. Obeys the statement, because when 20 + 15 is divided by 15, the remainder is 5. The answer to the question is 1.
case 2: D = 20, C = 15, N = 1. Obeys the statement, because when 20+15 is divided by 15, the remainder is 5. The answer to the question, however, is 5.

We have two different possible answers to the question for statement 1, and two different possible answers for statement 2. Now let's put them together.

(1+2)
case 1: D = 19, C = 14, N = 1.
- Obeys statement 1 (we already tested it).
- It also obeys statement 2, because when 19 + 14 is divided by 14, the remainder is 5.
- The answer to the question is 5.

case 2: D = 25, C = 6, N = 5.
- Obeys statement 1: 26 divided by 7 has a remainder of 5.
- Obeys statement 2: 125 divided by 30 has a remainder of 5.
- The answer to the question is 1.

So, the answer is (E).

That said, on the test, I would work on this one for about 90 seconds and then guess either C or E.
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Re: If N, C, and D are positive integers, what is the remainder  [#permalink]

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28 Oct 2017, 11:05
N,C,D are positive integers.
d/c =quotient + rem. We need to find remainder.

1) D+1/C +1 = 0 + 5
--> D = 9, C = 2. 7+1/3 = 0+ 5. D/C =9/2 = remainder = 1
--> D = 10+1, C = 5+1 --> 11/6 = 0 +5 = D/C = 10/ 2 --> no remainder

So NS

2) (ND + NC)/ NC = q + 5 --> ND +1 = q + 5 -->ND = 4. what is D and N?

1) 2) --> still no value to C,D,N. So E
Re: If N, C, and D are positive integers, what is the remainder &nbs [#permalink] 28 Oct 2017, 11:05
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